Density of a liquid in CGS system is `0.625(g)/(cm^3)`. What is its magnitude is SI system?

Options

A. `0.625`
B. `0.0625`
C. `0.00625`
D. `625`

Answer

To convert the density of a liquid from the CGS system to the SI system, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the given density in CGS units**:
The density of the liquid is given as \(0.625 \, \text{g/cm}^3\).

2. **Convert grams to kilograms**:
We know that \(1 \, \text{g} = 0.001 \, \text{kg}\). Therefore, we can express the density in kilograms:
\[ 0.625 \, \text{g/cm}^3 = 0.625 \times 0.001 \, \text{kg/cm}^3 \]
This simplifies to:
\[ 0.000625 \, \text{kg/cm}^3 \]

3. **Convert cubic centimeters to cubic meters**:
We know that \(1 \, \text{cm}^3 = 10^{-6} \, \text{m}^3\). Thus, we can convert the density:
\[ 0.000625 \, \text{kg/cm}^3 = 0.000625 \, \text{kg} \times \frac{1}{10^{-6} \, \text{m}^3} \]
This can be rewritten as:
\[ 0.000625 \, \text{kg/cm}^3 = 0.000625 \times 10^{6} \, \text{kg/m}^3 \]

4. **Calculate the final density in kg/m³**:
Now, we calculate:
\[ 0.000625 \times 10^{6} = 625 \, \text{kg/m}^3 \]

5. **Final Answer**:
Therefore, the density of the liquid in SI units is:
\[ 625 \, \text{kg/m}^3 \]

### Summary:
The magnitude of the density of the liquid in the SI system is \(625 \, \text{kg/m}^3\).